Question

determine wheter the series converges or diverges.

Answer 1

\[ \sum_{n=2}^{\infty} \frac{ 1 }{ n \sqrt{4}{ n } }\]

Answer 2

the denominator is supposed to be n(n^(1/4)) not 4n.

Answer 3

Converges at zero, since the denominator will end up being infinity and any constant over infinity approaches zero indefinitely.

Answer 4

I haven't done summation notation in awhile and I'm not a teacher, so if you don't understand something just ask.

Answer 5

sorry about that, computer cra pped out. i dont understand how you ccan tell that by looking at it.

Answer 6

The way that summation notation works is you take the number above the sigma and the number that n is equal to, below the sigma, in this case 2. And add one to the number below until you reach the number up top. So if you had the number 10 up top and the number 0 below you would do the problem 11 times, first by putting in 0, then 1, then 2, then 3... 9, 10.

However in this case since you're putting in infinity you aren't expected to do the problem forever, you can just know that you will end up with infinity for n. This makes it easy to tell that the denominator will end up being infinity since there are no variables in the numerator.

Answer 7

so what if there are variables in the numerator?

Answer 8

Your class will most likely cover that sometime soon, I assume you're in a pre-calculus class, which means they will begin talking about indeterminate form soon. However, if you're in an algebra II class then you won't need to know it for your class, but you can look it up if you're interested.

Answer 9

My previous claim only pertains to when the variable is approaching infinity.

Answer 10

im actaully taking my third semester of calculus in university hahahah.

Answer 11

Haha, everyone needs a bit of review.

Answer 12

i just need to pass lol.

Answer 13

The indeterminate form can often be eliminate if you have an n in the numerator and an n in the denominator, you may need to do some algebra in order to cancel out the n up top before you put your infinity in.

Answer 14

I hope this helps, you can feel free to message me, I have to be off now though.

Answer 15

thank you so much! bye!